Invariants
Level: | $120$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (of which $4$ are rational) | Cusp widths | $1^{2}\cdot2\cdot3^{2}\cdot6\cdot8\cdot24$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24G1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}5&6\\14&97\end{bmatrix}$, $\begin{bmatrix}52&59\\61&78\end{bmatrix}$, $\begin{bmatrix}65&36\\72&53\end{bmatrix}$, $\begin{bmatrix}73&84\\0&1\end{bmatrix}$, $\begin{bmatrix}84&23\\23&108\end{bmatrix}$, $\begin{bmatrix}119&42\\56&61\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.48.1.zz.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $12$ |
Cyclic 120-torsion field degree: | $384$ |
Full 120-torsion field degree: | $368640$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
12.48.0-12.g.1.3 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.24.0-120.bb.1.14 | $120$ | $4$ | $4$ | $0$ | $?$ | full Jacobian |
120.48.0-12.g.1.20 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
120.192.1-120.rk.1.28 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.rk.2.27 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.rk.3.28 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.rk.4.27 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.rm.1.24 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.rm.2.22 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.rm.3.24 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.rm.4.22 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.su.1.30 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.su.2.29 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.su.3.28 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.su.4.27 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sw.1.28 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sw.2.26 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sw.3.24 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sw.4.22 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.3-120.fy.1.41 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.hs.1.19 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.kv.1.31 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.kw.1.26 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.lu.1.23 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.lx.1.10 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.mp.1.29 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.mq.1.10 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.ok.1.21 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.on.1.19 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.pb.1.25 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.pc.1.19 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.pi.1.23 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.pl.1.34 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.ql.1.29 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.qm.1.18 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.sr.1.14 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.sr.2.12 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.sr.3.30 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.sr.4.28 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.st.1.15 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.st.2.14 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.st.3.31 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.st.4.30 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.tp.1.12 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.tp.2.12 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.tp.3.24 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.tp.4.24 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.tr.1.14 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.tr.2.14 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.tr.3.28 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.tr.4.28 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.288.5-120.bei.1.47 | $120$ | $3$ | $3$ | $5$ | $?$ | not computed |
120.480.17-120.brj.1.27 | $120$ | $5$ | $5$ | $17$ | $?$ | not computed |